SOLUTION: Rajesh would like to buy his first car and the one he has his eye on is $25,000, plus an extra 13% HST for a total price of $28,250. The dealership has a deal for $0 down payment a

Question 1190286: Rajesh would like to buy his first car and the one he has his eye on is $25,000, plus an extra 13% HST for a total price of $28,250. The dealership has a deal for $0 down payment and charges 2.79% interest on the loan. Rajesh plans to make car loan payments weekly and has accepted the maximum loan repayment period of 8 years.
How much will his weekly care loan payment be?
How much will he have paid to the dealership by the time his loan is paid off?
How much interest will be paid?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Rajesh is loaned $28,250 and must pay this amount back, plus interest.

There are roughly 52 weeks in a year
Over the course of 8 years, that will be 52*8 = 416 weeks total.
That means Rajesh has n = 416 car payments to make.

The annual interest rate is r = 2.79% = 0.0279
The weekly interest rate is r/52 = 0.0279/52
I'll leave it as a fraction like that.

The formula to calculate his payments is

L = loan amount = 28,250
i = interest rate per period = 0.0279/52
n = number of periods = 416

Crunching the numbers gets the following

approximately

Rajesh will have a weekly car payment of $75.79

If that amount is paid per week for 416 weeks, then 416*75.79 = $31,528.64 is paid back overall.

The difference of that figure and the amount loaned is the total interest
31,528.64 - 28,250 = $3,278.64

Extra info:
The effective interest rate is roughly 11.61% interest because (3278.64)/(28250) = 0.1161 = 11.61% which is much higher than the 2.79% stated APR.
The reason why the large jump is because Rajesh decided to go for the max length of the loan repayment. The longer the loan is in existence, the more interest there is to be made from it (hence the higher effective interest rate).
The trade off however is that he has lower weekly payments.

=====================================================

Answers:
Weekly payment is $75.79
How much is paid off in total? $31,528.64 (principal + interest)
How much interest will be paid? $3,278.64

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